Question

Question #7c8db

Answer 1

Whether you use `a_c=v^2/r` or `a_c=omega^2r` depends on the manner in which the velocity or acceleration is stated.
Details follow...

Explanation:

In this problem, the acceleration is stated in `"metres per second"^2`. This determines the units and also the form of the relation you must use, namely:

`a_c=v^2/r` f

Had the acceleration been stated in `"radians per second"^2`, you would use the `a_c=omega^2r` form.

Both formulas would yield the same result, of course, because `v` increases as `r` increases, but `omega` does not.

In other words, when `r` doubles, `v^2` increases by `2^2` times, and `v^2/r` increases by two times.

When `r` doubles, `omega` does not change, so `omega^2r` doubles.

Finally, in the last part of the question, if `omega` is doubled, then `omega^2r` increases by `2^2`.

Hope that clears it up.